Question

Find the lateral area of the following cone.Leave your answer in terms of pie

Answer 1

Recall that we are given the following cone

to use the formula of the lateral area (pi*r*l) we shoudl determine the value of r and l. From the picture, we see that the given radius is r=5. Also, we can see that we have the following right triangle

Since it is a right triangle, we can apply pythagoras theorem, so we get the equation

$l^{2}=12^{2}+5^{2}=144+25=169$

Applying the square roots on both sides, we get

$l=\sqrt[]{169}=13$

Then, the value of l is 13. Using the formula, the lateral area is

$r\cdot\pi\cdot l=(5)\cdot\pi\cdot(13)=65\cdot\pi$

So it has an lateral area of 65 pi squared centimeters.